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Lower entropy factors of sofic systems

Published online by Cambridge University Press:  19 September 2008

Mike Boyle
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195, USA
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Abstract

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A mixing subshift of finite type T is a factor of a sofic shift S of greater entropy if and only if the period of any periodic point of S is divisible by the period of some periodic point of T. Mixing sofic shifts T satisfying this theorem are characterized, as are those mixing sofic shifts for which Krieger's Embedding Theorem holds. These and other results rest on a general method for extending shift-commuting continuous maps into mixing subshifts of finite type.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

[1]Adler, R. L. & Marcus, B.. Topological Entropy and Equivalence of Dynamical Systems. Memoirs Amer. Math. Soc. 219 (1979).Google Scholar
[2]Denker, M., Grillenberger, C. & Sigmund, K.. Ergodic Theory on Compact Spaces. Lecture Notes in Math. 527. Springer-Verlag: Berlin, 1976.CrossRefGoogle Scholar
[3]Fischer, R.. Graphs and Symbolic Dynamics. Topics in Information Theory (Second Colloq., Keszthely, 1975), (ed. Csiszar, I. & Elias, P.), pp. 229244. Colloq. Math. Soc., Janos Bolyai, Vol. 16, North-Holland, Amsterdam, 1977.Google Scholar
[4]Kitchens, B. P.. Ph.D. Thesis, University of North Carolina, Chapel Hill (1981).Google Scholar
[5]Krieger, W.. On the subsystems of topological markov chains. Ergod. Th. & Dynam. Sys. 2, (1982), 195202.CrossRefGoogle Scholar
[6]Krieger, W.. On the Subsystems of Topological Markov Chains. Talk given at AMS conference ‘Ergodic Theory and Applications’,Durham, New Hampshire, U.S.A.,June 1982. Unpublished.CrossRefGoogle Scholar
[7]Marcus, B.. Sofic systems and encoding data. Preprint, (Department of Mathematics, University of North Carolina, Chapel Hill (1982)).Google Scholar
[8]Weiss, B.. Subshifts of finite type and sofic systems. Monatsh. Math. 77, (1973), 462474.CrossRefGoogle Scholar